Matrix Preconditioning Techniques and Applications

Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen’s book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers’ understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.

Spis treści:
1. Introduction
2. Direct methods
3. Iterative methods
4. Matrix splitting preconditioners [t1]
5. Approxi,ate inverse preconditioners [t2]
6. Multilevel methods and preconditioners [t3]
7. Multilevel recursive Schur complements preconditioners
8. Wavelet preconditioners [t5] for ˆA n x n and ˆA -1 n x n
9. Wavelet Schur preconditioners [t6]
10. Implicit wavelet preconditioners [t7]
11. Application I - acoustic scattering modelling
12. Application II - coupled matrix problems
13. Application III - image restoration and inverse problems
14. Application IV-voltage stability in electrical power systems
15. Parallel computing by examples.